Liquid crystals are useful as optical elements as their birefringence properties can be tuned electronically. Many applications of this technology, such as spherical and cylindrical lenses, require a variable retardation across the surface of the liquid crystal cell. One way of obtaining this variable retardation is to produce a spatially variable pretilt angle in a liquid crystal cell. The pretilt angle determines the alignment of the liquid crystal molecules in the bulk of the liquid crystal layer, which determines the retardation of the liquid crystal layer.
While it may be possible to create spatial variation of the pretilt angles by mechanically controlling the rubbing density of a polyimide alignment layer, doing so would be limited to producing one-dimensional variation and would only be practical for very small regions. While it is also possible to create spatial variation by combining a vertical alignment layer with a region of continuous horizontal alignment, creating the spatial variation in the boundary where the vertical alignment portion abuts the horizontal alignment portion, this would produce only a very limited region where spatial variation in pretilt angle is possible and would only be practicable for extremely small lenses.